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Deep learning on nuclear mass and $α$ decay half-lives

Ab-initio calculations of nuclear masses, the binding energy and the $α$ decay half-lives are intractable for heavy nucleus, because of the curse of dimensionality in many body quantum simulations as proton number($\mathrm{N}$) and neutron number($\mathrm{Z}$) grow. We take advantage of the powerful non-linear transformation and feature representation ability of deep neural network(DNN) to predict the nuclear masses and $α$ decay half-lives. For nuclear binding energy prediction problem we achieve standard deviation $σ=0.263$ MeV on 10-fold cross validation on 2149 nuclei. Word-vectors which are high dimensional representation of nuclei from the hidden layers of mass-regression DNN help us to calculate $α$ decay half-lives. For this task, we get $σ=0.797$ on 100 times 10-fold cross validation on 350 nuclei on $log_{10}T_{1/2}$ and $σ=0.731 $ on 486 nuclei. We also find physical a priori such as shell structure, magic numbers and augmented inputs inspired by Finite Range Droplet Model are important for this small data regression task.